High resolution synthetic irradiance is of interest for theoretical studies such as grid integration of solar PV and battery storage analysis. Access to site-specific data is often limited to inadequate temporal resolutions for such application. A new model for producing synthetic solar global horizontal irradiance (GHI) time-series at up to 1-min resolution is presented as derived from >10-min input data. Briefly, it is a clustered-based method for daily clearness index distributions using Dirichlet process Gaussian mixture model (DPGMM). DPGMM is a non-parametric Bayesian (NPB) model indexed with an infinite-dimensional space of parameters. The key benefit of the NPB paradigm is the automatic adaptation to the correct complexity level and model size, suggesting a local adaptation of the model to all climatic conditions. A posterior inference using Markov chain Monte Carlo algorithm (namely Gibbs sampling) is applied. The model only requires a valid number of intraday data to construct daily distributions, then it can be applied worldwide. The synthetic GHI time series are validated against observed 1-min GHI data for four locations distributed throughout the world with different climatic conditions and significant geographic separation. Moreover, the presented method can generate data based on similar climatic conditions. A good fit between real and generated data is observed. We present an nRMSE <= 4% and nMBE < +/- 4% between generated and measured means at both daily and monthly scales for all sites. The agreement between the real and generated cumulative density distributions of six comparative variability metrics (defined in text) at four different sites is measured using the overlapping and the Kullback-Leibler coefficients, which are >= 75% and <= 10% respectively, in all cases. To ensure the reproducibility of the research presented in this paper, the methodology is freely available as an R-package downloadable from SolarClusGnr.